"Mister Joker, Doctor Schiller, this rule indeed seems a bit unfair to Ms. Carrol. However, I think while the rules dictate the order of throwing matchsticks, they do not strictly stipulate how many each person should throw, we could throw 1~3."
"In this case, why don't we simply use another game to determine the number of matchsticks thrown, how about it?"
Katy held her hands together as she spoke, looking a bit nervous, glancing at the angry Carol next to her, then at the careless face of Joker, and finally resting her gaze on Schiller's face.
Schiller patiently smiled and asked, "So, which game do you think would be suitable, Miss Katy?"
"Why not rock, paper, scissors," Katy proposed hesitantly. "We take turns to compete against Ms. Carrol. If you win, you decide how many to throw, and if you lose, Ms. Carrol decides."
"Why should we do that?" Joker slammed the table and said, "As long as we play according to the rules, we will win, and the stupid woman will die from an explosion. What's the point of playing Rock, paper, scissors?"
"I've already told you, if you don't give me a fair rule, I'll raise the fire, and burn the house!"
"I also told you, as long as we don't let the match ignite the flames, raising the fire will be in vain!"
The situation resulted in a stalemate, but thankfully there was no rush from the host. It seems the game doesn't have a time limit. However, dragging on like this isn't a solution.
The outcome they all discussed before the game began was the same. The one to make the first move in the whole game possesses a considerable advantage. Dragging a game for too long will miss the chance to watch other teams.
Just as Katy was about to step in and mediate, the doctor on the opposite side spoke, "Staying in this stalemate isn't a solution. But if it is as Miss Katy suggested, everyone would have a game of rock, paper, scissors with Ms. Carrol once. That seems to give Ms. Carrol too much of an advantage."
Carol was a bit stunned. She actually hadn't understood the rule proposed by Katy. She was busy arguing with Joker on the other side. Now that Schiller had repeated it, she finally realized.
After giving her a look, Katy sighed in frustration. Carol wasn't proving to be a good teammate. Katy originally wanted to propose a rule that would give Carol a significant advantage, but others disagreed, so she suggested a more conservative one.
If Carol grasped her intentions, she would know that it would be best to form an alliance at this moment, make a move while the iron is hot and make the additional game a reality, which could then reverse their disadvantageous situation.
Unfortunately, Katy's plea fell on deaf ears. Carol's brain only allowed her to focus on one thing at a time. She was so busy arguing with Joker, she didn't even try to understand Katy's rules.
Now that she reacted, she went to think carefully, but she still didn't understand how having each person take turns to play rock, paper, scissors against her gave her an advantage.
Seeing Carol's puzzled reaction, Katy sighed deeply, knowing that Carol simply didn't know how much of an advantage this rule would bring her.
Truth be told, if someone on the opposite side was foolish enough to agree to this rule, Carol would undoubtedly win.
From a probability point of view, the chances of winning a game of rock, paper, scissors are 50% for each side. If paired randomly, not affected by any external factors, everyone's composite win rate is constant.
However, if a person takes turns playing rock, paper, scissors with three other people in a round, and others only play once in a round, although the person's win rate against every other person remains 50%, the fact that this person plays more games means the composite win rate will be higher than a single game's win rate.
The most advantageous factor is that if she wins, Carrol decides by herself how many to throw, and if she loses, they have to do as she says. The maximum limit for throwing matchsticks is three. Even if she wins, she only has to play according to the rule which benefits her the most. If she loses, besides throwing one stick, she could also instruct not to throw any and directly skip.
That way, it clearly increased Carol's bargaining chip to threaten others with burning the house. If she skips all her turns, she won't necessarily burn down the house.
However, if she can instruct others to skip, as long as she wants, she can definitely burn it down then, she would become the undoubted ruler of this game, with the power to threaten others with a lose-lose situation.
After half a day of contemplation, Carol didn't manage to figure it all out. She did vaguely feel that this rule was better than the current situation. So, she said, belatedly realizing, "Let's do it this way! This is fair to me!"
"Stop dreaming, you stupid woman!" Joker immediately scoffed. "Why should we listen to you? You're just a poor loser waiting to be eliminated. The sooner you die, the better."
Without mentioning how Carol was thwarted into a furious rage, Schiller spoke with a hint of resignation.
"Calm down, everyone, this will lead to a dead end, why not listen to my suggestion?"
The three of them focused their gaze on him. After a moment's hesitation, Schiller said, "I think rock, paper, scissors is a good method. The number of games should be equal, though. Why not take turns to play against the person next to us. The winner decides how many the loser throws, it would be much fairer."
Katy's eyes widened in shock. She didn't understand why Schiller would propose such a rule. If they did this, wouldn't she, being Carol's predecessor, be severely disadvantaged?